Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach

摘要

In this work, we discuss some theoretical and numerical aspects of solving differentialudequations with discontinuous right-hand sides of Filippov type. In particular, (i) we propose secondudorder corrections to the theory of Filippov, (ii) we provide a systematic and nonambiguous way touddefine the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, andudimplement, a numerical method to approximate a trajectory of systems with discontinuous right-handudsides and illustrate its performance on a few examples.